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Later
Gross Chess. A big variant with a small learning curve. (12x12, Cells: 144)
Aurelian Florea wrote on 2018-09-15 UTC

About promotion from my experience with the two apothecary games which I have designed and I had the promotion rules similar (although at the time I have forgotten the exact game from where I had took the inspiration) most often the rook is the piece of choice because on rare ocasions the extra move actually worth it. HG pointed that first to me and I tend to agree. But it is much more fuzzy probably than him and me actually though about it initially. Probably here is the same thing. But for promotion extra on the side material 1 queen, 1 rook and 1 knigh would be more than enough.

Greg Strong wrote on 2018-09-14 UTC

There was an error with the Average Mobility numbers - I have now updated the table.

The Average Mobility is a Betza Mobility Calculation with a board occupancy of 30%. Basically, for a piece that can only make a single step, the number of directions attacked and average mobility will be the same (as though the board was empty.) For each additional step in a given direction, though, the weight is that of the previous step multiplied by 0.7 (to approximate a 30% chance that the previous square was occupied.)

Kevin Pacey wrote on 2018-09-14 UTC

@ Greg

I'm curious how you estimate/calculate average mobility, if it's fairly simple to describe. I do this myself as one step when calculating my estimate for a knight's value on the (typically) rectangular or square board used for a given chess variant, by figuring out (and adding up) the number of squares a N can reach on an empty board from every single square, then calculating the average number of squares a N can reach on the board, if it were placed on each square one at a time. In Gross Chess, for example, there are a lot of squares from which a N can reach either 8 or 6 squares. Fwiw, I didn't bother to work out the exact average just yet, but estimated it must be around at least 6 squares (out of the impossible to reach 100% full mobility score, or 8, max.) for a N on an empty Gross Chess board. This seemingly isn't compatible with your 4.89 score for the N, but it does seem it could match your Average Directions Attacked figure for the N. [edit: your mobility score for a pawn in Gross Chess is a clue that you're somehow taking into account the average number/positioning of enemy and/or friendly forces on the board, too, though in that case I still don't quite get why the Vao and Cannon mobility fields are left empty in your posted table.]

[edit: Otherwise I'd note that I have a Cannon as 1/2 the value of a R (as it is in Chinese Chess), and similarly I have a Vao as 1/2 the value of a B. I'd also note that much earlier in this Gross Chess thread, Mr. Paulowich gave his own estimates for the piece values.]

Greg Strong wrote on 2018-09-14 UTCExcellent ★★★★★

This is an excellent game. I avoided it for a long time because I thought the large amount of power on the board would make it too difficult for me to deal with. It turns out I find it very playable, although it does require me to spend more time thinking before making a move for most of the game. Midgame positions can be exceptionally complex.

The opening starts out feeling nice and slow, as though the first 10 or so moves don’t matter too much. While I think it’s true that there is a very large amount of flexibility to how you can play the opening, those moves are still very important. At some point, typically around move 20, the game breaks open and becomes tactical and violent quickly. You want your pieces well-positioned when that happens. There is some contention for the e4/e9 and h4/h9 squares. All three of the light leapers – Champion, Wizard, and Knight – are good to develop early and all three are natural to develop to those squares, so you must choose which to develop there. I find that typically one of these three piece types doesn’t get developed in the opening before the game gets wild. I think it’s important to get the Vaos developed early. By the endgame, they are the weakest piece, but their low material value and ability to make long-range jumps gives them significant power to harass the heavier pieces as the game progresses. Developing the Vaos generally requires developing the Knights.

I like the promotion rules overall but the 14 extra pieces each player starts with in reserve seem unnecessary. There is tremendous carnage before any pawns are in a position to promote so lack of replacements is not an issue. The extra Queens are the only pieces that have any realistic possibility of being used.

Well-played games are typically nail-biters and the dynamic between the two players can reverse several times before it’s over. Having the momentum is very important – you want to be the one forcing the opponent to react, and the longer you can keep it that way, the more advantage you will accumulate.

My estimage of the piece values:

 Piece Ave. Dir. Attacked Ave. Safe Checks Ave. Mobility Midgame Value Endgame Value Queen 7.03 29.03 17.33 12.5 13.5 Marshall 9.78 24.44 15.79 10 11 Archbishop 9.47 16.81 13.76 8.5 9 Rook 3.67 18.33 9.68 6.5 7.5 Champion 9.78 6.11 9.78 6 6 Wizard 8.86 5.50 8.86 6 5.5 Bishop 3.36 10.69 7.65 5 5.5 Cannon 5 2.5 Vao 3.5 1.5 Knight 6.11 6.11 6.11 2.5 2.5 Pawn 1.68 0.00 1.68 1 1.25

Kevin Pacey wrote on 2018-09-14 UTC

For now I'd estimate the piece values in Gross Chess on average (or at least in the endgame) to be: P=1; V=1.9; N=2.6; CA=2.75; CH=2.8; W=3.4; B=3.75; R=5.5; A=7.4; M=9.1; Q=10.25; K's fighting value = 1.8.

Aurelian Florea wrote on 2018-08-14 UTC

When you get into 5-6 pieces pawnless endings it probably get really tricky :)!

H. G. Muller wrote on 2018-08-10 UTC

Interesting questions. I hacked my 4-men EGT generator to also handle hoppers. It indeed says that in KVNK, KCCK and KNNK mate can in general not be forced. For the latter this always hold: there are no forced mate-in-2 position on boards of any size. KCCK in addition has some forced mate-in-2 positions (when the bare King already starts in a corner, pushed against the edge by the other King). For KVNK there are some longer forced mates, of up to 16 moves, but the positions that are lost for the side to move make up only 0.2% of all positions on 8x8, and less than 0.05% on 12x12.

KCNK and KCBK are generally won, though. (Max DTM 50 and 39 moves on 12x12, respectively.) For comparison, KBNK takes at most 64 moves on 12x12.

I had no easy way to check if the results are correct, as the program only produces statistics (number of mate-in-N and mated-in-N for each N), and does not contain code to probe the DTM or best move for a specific position. The hack seemed simple enough, though. (Just skip to the first occupied square in the applicable direction before starting to generate captures in the normal way.)

Greg Strong wrote on 2018-07-28 UTC

Yes, by a large margin.  Zillions is so universal that it has basically no specialized chess knowledge.  It also hasn't been updated in about 15 years and chess programming techniques have improved a lot in that time.

Fergus Duniho wrote on 2018-07-28 UTC

Is Chessv stronger?

Greg Strong wrote on 2018-07-27 UTC

Although I believe it is correct that those combinations cannot force mate, testing with Zillions means little.  It's skill level is very low.

Fergus Duniho wrote on 2018-07-26 UTC

I left Zillions-of-Games running again, this time with a Knight, a Vao, and a King for White against a lone black King. I then forgot about it until I was ready to turn the computer off for the night. I just stopped it on turn #1986. So, clearly, a Knight and a Vao are not sufficient mating material.

I based my original judgments on whether I could conceive of checkmates that used the pieces in question. For example, if the Black King were on a12, the White Vao was on the diagonal for that space, say at h6, and the White Knight moved to c10, that would be checkmate. The difficulty is in getting the lone King to stay in a corner where it can be easily checkmated in this way. I'll have to run more trials with Zillions-of-Games to see what combinations of material can actually force checkmate.

Fergus Duniho wrote on 2018-07-25 UTC

I have been letting Zillions-of-Games run with two Knights and a King for White against a lone King for Black, and it has played over 200 moves so far without a checkmate. So, it's not looking good for this combination of pieces either.

Fergus Duniho wrote on 2018-07-25 UTC

It looks like you're right about the Cannons. I have been running Zillions-of-Games with a King and two Cannons for White and only a King for Black. Having finished something else I was working on, I just remembered I had it running, and it is has gone for nearly 600 moves without checkmating the King, which is well over the 50-moves limit.

Prussia General wrote on 2018-07-25 UTC

Sufficient Checkmate material:

Fergus said that Cannon could checkmate with any other minor piece. I have tested this myself and confirm that K+C+N and K+C+B could indeed force checkmate. How do you force a checkmate with two cannons? I tried it out; and although I could trap the king in the corner, checkmate could not be forced so I'm curious how you did that.

Fergus also said that checkmate could be done by two knights. It is well known in FIDE chess that checkmate could not be forced. Is there some additional rules in this variant that I'm missing?

Also how do you guys value Cannon comparing to Knight and Bishop? In Chess P-N-B-R-Q is valued 1-3-3.5-5.5-10 and in Chinese chess P-N-C-R is valued 2-4-4.5-9 but these are some what different scales.

Thanks!

Kevin Pacey wrote on 2018-03-16 UTC

Today I was toying with the thought of what if this variant were played on a 12x10 board, but then I couldn't conceive of an arguably nice setup where the Vaos are not peering into the enemy camp beyond the pawn-line. Thus it seems 12x12 is a good board size fit for the selected armies of this variant.

Kevin Pacey wrote on 2018-03-07 UTC

Thanks H.G.

If I think I can use my (12x8) Wide Nightrider Chess and (10x10) WAD Chess variant ideas after all (see the diagram testing thread) then the info you've provided about the WAD's mating potential on these size boards will nicely be of assistance.

H. G. Muller wrote on 2018-03-07 UTC

Usually it is the narrowest dimension that counts, although the largest dimension will then affect how long it takes. When you can push the bare King towards the small edge, you can just repeat doing that as often as is necessary. (For symmetric pieces. With asymmetric pieces it is more complex.)

Just to be sure I checked it out, and the WAD on 12x8 can force mate in maximally 37 moves. Even its weaker cousin the WD can force mate there (43 moves).

Kevin Pacey wrote on 2018-03-07 UTC

@ H.G.: I'm not 100% clear on whether champion+K cannot always force mate on a 12x8 board (which might be called bigger than 10x10 due to the greater width, though 10x10 has more squares in total). Might you happen to know?

Also, I noticed on the Omega Chess commercial page somewhere that champion+K cannot [always] force mate in that variant, but no doubt that's because of the 4 extra squares added to the board edges, at the corners. It's also noted there, as I long ago figured out, that R+K cannot always force mate, either, though it's often possible I suppose.

Fergus Duniho wrote on 2018-03-06 UTC

Okay, I'm not much into westerns, but I guess it means in this context, the group of pieces trying to checkmate the King.

H. G. Muller wrote on 2018-03-04 UTC

> I'm guessing H.G. actually meant to spell the word 'posse' instead, i.e. use one more 's'.

Ah yes, I am sorry. It is a word I only know from watching westerns, and I had never seen it written down. Of course I should have known that 'pose' according to English pronounciation rules would sound different, and actually is an existing word. I corrected the spelling now in my original posting, thanks.

Kevin Pacey wrote on 2018-03-04 UTC

I'm guessing H.G. actually meant to spell the word 'posse' instead, i.e. use one more 's'.

Fergus Duniho wrote on 2018-03-04 UTC

This is interesting, but I don't understand what the word pose means in this context.

H. G. Muller wrote on 2018-03-03 UTC

When programming is involved one can never be completely sure. But it is what the EGT generator says, and that same generator gives exactly the right statistics for the conventional pieces (where other EGT exist to compare against). The number of positions at each DTM then is exactly the same.

What I am sure of is that the argument you give is not relevant. What is relevant is whether the bare King can outrun the 'posse' that tries to drive it in the direction where it doesn't want to go, and run circles around it. If the mobility of the exclusion zone created by the attacking pieces is larger than the speed of a King, the latter is effectively trapped on one side of it. The point is that the board has edges. So it is enough if your posse can keep up with the King when it stays running in the same direction. Because eventually it will be blocked by an edge, and will have to reverse. Which takes some extra moves before you have to start keeping up with it, which can be used to make progress. E.g. King + Bishop + something vs King: King + Bishop can confine a King in a triangle at a corner, because the attacking King can plug the hole where the bare King could slip through the Bishop diagonal. But is just moves fast enough to keep doing that. But when the bare King has to reverse because it hits the edge, it now needs two moves before it threatens to escape, so you have one spare move to approach your third piece. Eventually it will then join the posse, and force the bare King to step back rather than just reversing, at an edge. This will work on a board of any size.

But when the speed of the posse is lower than that of the bare King, you can no longer confine the latter when the number of moves it needs to gain the width of the posse is smaller than what the posse needs to cross the entire board.

P.S. The entry form throws away long stretches of text again. Luckily I has moved this one to the clipboard before pressing 'Preview'....

Greg Strong wrote on 2018-03-03 UTC

Are you sure?  It does not make sense to me why a mate could be forced on 10x10 but not on 12x12.  Both sizes are much, much larger than the max range of either piece (range 2).

Kevin Pacey wrote on 2018-03-03 UTC

Thank you H.G.

Now I can rest assured that for a 10x8 variant idea I'm toying with, a Champion can always force mate, while for Gross Chess' 12x12 board it cannot.

Later